almost all of it has been drunk by at least one dinosaur.
I'm skeptical. While Randall doesn't say it explicitly, he seems to assume that a water molecule is effectively indestructible. But we know that's not true, and 65 million years is a long time. I mean, there's all sorts of chemical reactions that use H2
O as either as input or an output. If you convert some H and some O into other chemicals and later break those down and produce more water, as I'm given to understand many of us do all day long, I don't think you can count this "Molecule of Theseus" as the same one the dino drank.
Indeed. Plants are constantly turning water into sugar and other important organic molecules (converting carbon dioxide to oxygen in the process), and animals are constantly converting those organic molecules into other organic molecules and oxidizing them back into carbon dioxide & water. Furthermore, in liquid water the molecules themselves are constantly ionizing and deionizing via the reaction 2H2
O <=> OH-
. I suspect, but do not know, that these two kinds of reactions represent the majority of chemical reactions that water molecules participate in on Earth.
I have no idea how to estimate the rate of water-water ionization reactions, but global warming research provides a good window on the rate at which water is converted into carbohydrate, because that is the same as the rate at which carbon dioxide is converted into carbohydrate. According to the IPCC Third Assessment report
, "The amount [of carbon dioxide] that is 'fixed' from the atmosphere, i.e., converted from CO2 to carbohydrate during photosynthesis, is known as gross primary production (GPP). Terrestrial GPP has been estimated as about 120 PgC/yr [PgC = petagram carbon]." This means about 180 petagrams of water are consumed (since H2
O molecules react one-to-one with CO2
molecules in plant respiration, and an H2O molecule weighs 50% more than a carbon atom). This is 180,000 km3
, about 1/8000 of the total volume of water on the planet. Even if only one water molecule in 8000 reacts in a given year, then each water molecule has a roughly 1 in 107600
chance of surviving for 140 million years.* As there are fewer than 1050
molecules of water on the planet, none of them have been around since the Jurassic.*Assuming events are independent. This is not true, because some water, e.g. water frozen in glaciers, may remain stable for millions of years. So there may be a little water remaining that has been water since the time of the dinosaurs, but likely only a very small amount.
I'm looking forward to the day when the SNES emulator on my computer works by emulating the elementary particles in an actual, physical box with Nintendo stamped on the side.
"With math, all things are possible." —Rebecca Watson